Misunderstanding Statistics
Today I ran across and article talking about relative risk of death in America vs. Americans traveling abroad. I won’t be linking the article because the point of what I am about to write isn’t the premise in the source, but the misunderstanding of the math involved. For the record I agree with her premise, but her math is wrong.
Let us look at the following quote:
Mass Shootings
A mass shooting is defined as, “FOUR or more shot and/or killed in a single event [incident], at the same general time and location, not including the shooter.” (Shooting Tracker)
In 2014, 271 people were killed from mass shootings in America. In 2015, there were 333. In 2016, there were 383. In 2017, there were 346. (Gun Violence Archive)
THESE FIGURES ARE FROM FROM MASS SHOOTINGS ALONE.
Compare this average of 333 Americans dying per year from mass shootings to an average of 157 Americans getting killed via any type of homicide, anywhere abroad, per year.
*mic drop*
The author should have looked deeper and kept a hold on the mic. She is comparing two different populations but only thinking about one of them. In the “333 Americans die in mass shootings” the population of Americans is some 350+ million. In order for the two averages to be comparable virtually all American must also travel abroad, on average, every year. I am certain this is not the case. So many are?
Before answering, let us think about how many would have to be traveling abroad to make the two averages similar. According to the OP’s numbers 333 out of 350,000,000 Americans die in a mass shooting on average per year. This gives us a per-capita ratio of 0.95 people per million Americans. To make that per-capita the same for “Americans traveling abroad” how many Americans must do so, on average, per year? About 149 million Americans would need to be traveling abroad every year, on average, for the risk to be (close enough to) the same.
According to the data I found, less than half that number are. In 2016 we hit a record of 66,960,943 Americans doing so. The year before it was 61,783,913. In 2017 we 80 million. So lets be “generous” and apply an average traveler count of 70 million. Now what are the odds of getting murdered while traveling abroad? Well, the ratio with the above figures gives us 157 / 70,000,000 = 2.24 per million.
So for every one million Americans in the U.S. 0.95 die in a mass shooting. For every million Americans traveling abroad 2.24 get murdered. In which group, based on those numbers, would you choose to be in if those are your concerns? The reality is that you are more than twice as likely to get murdered while traveling abroad than to get murdered in a mass shooting in America. But that isn’t the end of the story.
To no rational person’s surprise that risk is destination dependent. If you were to guess, which is more likely to result in an un-natural death: going to Mexico or Canada? I’ve not found any data on how many Americans have been murdered in Canada, averaged or otherwise. However, the referenced Time article has this:
Now they do make refernces to total deaths as being possibly from 2002 to 2014. So if we take that 843 and average it out over twelve years we get 70.25/year. As a side note, see how poorly Time presented this data? The “Homicides reported’ column is aggregate but the visitor count is one year. Lets take an easy route of applying that second column as an average. That would mean for every million Americans who went to Mexico 2.71 of them will be the victim of homocide. More than twice the rate of mass shooting murders in the U.S. You are more likely to be murdered while traveling abroad than to die in a mass shooting in the U.S, and almost three times as likely if your destination is Mexico.
Then there is the Philippines with a rate of 11.75 per million per year, and Honduras and Haiti each of which have visitor rates so low they don’t show up at baseline in the data Time used. To get an idea of just how low it must be consider that the source report Time used didn’t have a listing for them and “Only U.S. origin areas having a sample size of 400 or more are displayed.” is the note on that. I’ll let you figure out the per-capita rate for Americans visiting Honduras if the size of that particular population is under 400. Hint: it isn’t small.
This is a major factor in my intense distrust of anyone use “averages” and our general reliance on them. Averages don’t really tell you anything useful outside of the literal metric — and often nothing useful at all. So much so that often if you rely on an average to make your point, you’re probably wrong. If you’re comparing averages across disparate populations, you’re highly likely to be wrong.
Indeed, even within the United States, you can’t really just apply a national average and per-capita to an individual situation. Mathematically speaking your risk of getting murdered by a mass shooter in Butte, Montana is zero since there have been none there. Thus your risk of getting murdered abroad is ridiculously higher than getting mass-murdered in Montana. Hell, your risk of dying while abroad is certainly higher than the risk of getting mass-murdered in Montana.
This represents the other fundamental flaw: using national averages for such a large geographic area against an even larger area.
The author could have made a more solid case by instead using actual homicides committed with a firearm rate than “mass shootings”, and used per-capita rates. Depending on which government source you use the per-capita rate for that is 22–32 per million for the U.S.. Much higher than the rate of murdered Americans abroad. But I suppose that wasn’t something she felt she could drop the mic for since that’d surprise nobody. Indeed, the overall homicide rate, gun or otherwise, is higher.
But I’d be wary of comparing that alone either. After all, we have six states with an overall homicide rate in 2017 of 2.0 or less. Nationally the U.S. averages 4.9 per 100,000 while the global average is 6.2 per 100,000. This brings us right back to destination being the most important factor. Consider this image I grabbed from Wikipedia:
Every single one of those is several factors higher than the U.S. These are per-hundred thousand, not per-million as was used for American travelers abroad.
So I agree with the general “don’t assume travel abroad is overly risky” idea, the reality is that you must make rational decisions based on actual data — or as close as we can get. Traveling to Canada is safer than to Mexico, which is safer than Venezuela or El Salvador.
The reason the murdered-abroad numbers are as low as they are is because most Americans remain on the continent. We tend to go to Mexico, Canada, and the U.K. Rounding out the top five are the Dominican Republic and France, respectively. To get a sense of scale here, in 13 years as of 2015 only 189 Americans in Canada had died compared to the 2,931 in Mexico.
Traveling to those places, even w/Mexico’s rates, is still safer than living in Washington D.C. if you’re looking at homicide rates. I say “living in” because I don’t have data on homicide rates for visitors to D.C, but the rate overall for D.C. is 24.2/100,000 which is certainly higher for staying in North America — but still lower than Honduras or even South Africa.
That isn’t to say per-capita is a gold standard, I even have my doubts there. Particularly when the population size is dramatically different. I’m unconvinced that even per-capita lets you properly compare a population of 5,000,000 with one of 750,000. But it is certainly much better than using averages across dramatically different population sizes.
